The article singles out paying users. So there is a way to pay for OAI/Anthropic models without having the model trainers look at all you do, it's just not well known.
His gripe is not merely about training, but about them keeping the data around for N days for security audits - that's how last year Azure discovered how various accounts around the world were using LLMs to manipulate elections, etc.
Given that the article is recommending something called Tinfoil instead, I don't think that's particularly relevant here.